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Homework 3
Economics 503
Foundations of Economic Analysis
Practice
1.
Real Interest Rate Below is a table showing a nominal interest rate on bonds
that was prevailing in the December of each year from 1991-2005. Also shown is
the level, P, of the CPI index for 1991-2006. Assume that there is a fixed
equilibrium real interest rate in each period of 2.5% (r = .025). Use that estimate
to derive the forecast of inflation for the subsequent year. Use this to calculate, the
actual inflation rate in Hong Kong in the years 1992-2006. Calculate the ex post
real interest rate for HK for each year the period 1991-2005? In which years, was
the ex post interest rate greater than the ex ante real interest rate? In which years
was the ex post real interest rate negative?
P
Dec, 1991
Dec, 1992
Dec, 1993
Dec, 1994
Dec, 1995
Dec, 1996
Dec, 1997
Dec, 1998
Dec, 1999
Dec, 2000
Dec, 2001
Dec, 2002
Dec, 2003
Dec, 2004
Dec, 2005
Dec, 2006
i
73.1
79.9
86.8
94.6
100.8
107.6
112.7
111.1
108
105.9
99.4
100.3
99.1
99.7
101
102.9
5.18
5.47
4.26
7.74
5.54
5.58
9.6
5.96
6.37
5.42
3.41
1.763
1.125
0.993
3.983
3.519
2. Real Exchange Rate. Construct a real exchange rate for HK for the years 20022007. In 2002, the relative price of a market basket of goods in HK in HK$
relative to the price of goods in the US in US$ is HK$6.9 per 1 US$ while the
exchange rate is 7.8. Below is the CPI for HK and the US with base years of
2000.
Price: P
HK
2002
2003
2004
2005
2006
2007
100.3
99.1
99.7
101
102.9
103.2
US
180.9
184.3
190.3
196.8
201.8
207.92
In which years is the HK undervalued and which is it overvalued?
3. Money Market Assume there is a negative supply shock in the United States
which reduces real and nominal GDP. The central bank wants to conduct
monetary policy to stabilize the price level. Draw a picture of the money market.
Show how the money supply and demand curve would shift in response to these
events. What would happen to the money market interest rate and money supply?
4. Real Exchange Rate Growth The following chart shows the CPI in the USA and
Hong Kong for the years 2003-2008. Assume that the growth in Hong Kong’s
exchange rate is zero. Calculate the growth rate of the real exchange rate for
2004-2008. What is the average growth rate of Hong Kong’s real exchange rate
for those years?
CPI
USA
2003
2004
2005
2006
2007
2008
181.7
185.2
190.7
198.3
202.4
211.1
HK
101.3
99.8
99.5
101.3
103.3
106.7
5. Loanable Funds Market Some economists argue that the savings behavior is not
very responsive to the interest rate. Other economists argue that savings is
strongly affected by the interest rate. Use the loanable funds framework for a
large, closed economy. Compare the effect of expansionary fiscal policy (i.e. an
increase in government deficits) on the interest rate and investment in A) an
economy in which the supply of loanable funds (S) was inelastic with respect to
the interest rate; with the effect in B) an economy in which the supply of loanable
funds is very elastic. Draw a graph of each theory to show under which theory
there is a bigger impact on investment and under which theory there is a bigger
impact on the interest rate.
6. Foreign Exchange Market. Diamonds are discovered in Australia. Foreigners
want to buy these diamonds and need Australian dollars to do so. Assume that this
discovery has no particular effect on Australian demand for foreign goods or
assets. Draw two graphs of the Forex market: 1) Demonstrate the effect on the
Australian dollar exchange rate if Australian monetary policy remains unchanged
so the exchange rate is allowed to fluctuate; 2) Demonstrate the effect on the
market if the Reserve Bank of Australia conducts monetary policy to keep the
exchange rate from changing.
1.
he Organization of Economic Co-operation and Development (OECD) constructs
theoretical measures of potential output for most of the G20 countries and some others
which are used to develop projections in their semi-annually published Economic
Outlook publication. Gather information from the OECD Stats Extract website on the
output gap and unemployment rates in 2008 and 2009 from the following website
http://stats.oecd.org/index.aspx . On the left hand bar of menus, open the menu marked
OECD Economic Outlook and the sub-menu marked OECD Economic Outlook Current
and Recent Editions. Click on the link on that menu marked Economic Outlook No 86 December 2009 - Annual Projections for OECD Countries (or go directly to this link
http://stats.oecd.org/Index.aspx?DataSetCode=EO86_MAIN ). Under Current Data
Selection, Click on the link marked Variable [0/142]. This should bring up a selection of
menus. Open the menu called SUP:Supply Block and check GAP: Output gap of the total
economy. Open the menu called LAB: Labour markets and check UNR: Unemployment
rate. Choose under Time and Frequency years 2008 and 2009; Choose under Country,
10 countries including Australia, Canada, France, Germany, Italy, Japan , Netherlands,
Spain, United Kingdom, and USA. Download the data on the output gap and
unemployment rate by country for 2009. Fill in the following chart.
Output Gap
Unemployment Rate
AUS: Australia
CAN: Canada
FRA: France
DEU: Germany
ITA: Italy
JPN: Japan
NLD: Netherlands
ESP: Spain
GBR: United Kingdom
USA: United States
Calculate the cross-country correlation between the output gap and the unemployment
rate across countries.
2.
sing aggregate demand, short-run aggregate supply and long-run aggregate supply
curves, explain the process by which each of the following economic events will move
the economy from one long-run macroeconomic equilibrium to another. Illustrate with
diagrams. In each case, what are the short-run and long-run effects on the aggregate price
level and aggregate output?
a. There is a decrease in households’ wealth due to a decline in the stock market.
b. There is an increase in the wealth of households in the economy of a foreign
trading partner.
3.
Consider again the case (a) from the above problem, when household wealth
increases. Focus on how event (b) will change money market interest rates. Draw a graph
of the money market and show what would happen to money market interest rates after
event (1b) if the central bank left the money supply unchanged. (Hint: After event (1b),
GDP will change. How will this change affect money demand?).
4.
Obtain annual data on US real GDP, potential GDP, and the unemployment rate
from the US Congressional Budget Office Website (US Congressional Budget Office
Website ).
 Data on Real GDP with 2000 prices and the unemployment can be found in Excel
format by following the link at: Details of CBO's Year-by-Year Forecast and
Projections for Calendar Years 2009 to 2019 (Along with data for 1950 to 2006)
DATA
 Data on potential GDP with 2000 prices can be obtained by following the ling at:
Supplemental Information on Key Assumptions in CBO’s Projections of Potential
Output DATA
Calculate the output gap and the unemployment rate for the years 1950 to 2006. Calculate
the correlation between the two using the Data Analysis tool in Excel.
5.
In 2005, a hurricane hit New Orleans, Louisiana, an important transportation and
oil refining center in the USA, one of Hong Kong’s key for the petrochemical industry in
that country.
a. Consider the impact of the recent hurricanes that devastated that city as a
temporary supply shock for the USA. Discuss briefly, using one graph, the
outcomes that we would have been likely to see in terms of goods markets in
the USA as a result of this negative business cycle shock.
b. Analysts are also worried that the natural disaster might have had a negative
impact on consumer confidence. Discuss briefly, using one graph, the
differences in outcomes that we would observe if this demand side effect were
stronger from the outcomes that we would observe if the supply side effects
were dominant.
6.
Does the BOJ have a Taylor Rule? The following table shows numbers for
Japan’s inflation rate, output gap, and the uncollateralized call money interest rate for the
years 1990 to 2000.
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
i.
Output
Actual
Gap
Inflation
Interest Rate
3.30%
3.02%
7.56%
4.09%
3.22%
7.48%
2.50%
1.70%
4.82%
0.51%
1.26%
3.18%
-0.87%
0.69%
2.41%
-1.20%
-0.12%
1.15%
2.14%
0.13%
0.48%
2.32%
1.75%
0.52%
-1.48%
0.67%
0.44%
-2.46%
-0.33%
0.06%
-2.57%
-0.71%
0.12%
Calculate the inflation gap (i.e. the difference between inflation and target
inflation) in each period if Japan had used a target inflation rate of 2% in each
year. What is the average inflation gap during the period 1990-1995
(inclusive) and for 1996-2000?
ii.
Calculate the interest target, iTGT, for every period if the Bank of Japan had
used a Taylor rule as specified in class. Compare this with the actual interest
rate. Does the Bank of Japan adjust the target interest rate to domestic
inflation and output?
iii. Some have argued that the BOJ was not aggressive enough in cutting interest
rates in the early 1990’s to get the economy out of the slump. What was the
average interest rate during the period 1992-1997? What was the average
interest rate suggested by a Fed-style Taylor rule. Which was larger?
iv.
What difficulties did the Bank of Japan have in implementing the Taylor rule
in 1999 and 2000?
1.
Construct an AS-AD model of the economy. Begin by assuming the economy is
in a long-run level of equilibrium with the aggregate supply curve crossing the aggregate
demand curve at the level of potential output. Use the model to describe how each of the
events will change the macroeconomic equilibrium in the short-run. Suppose that
policymakers allow the self correction mechanism to bring GDP back to the long-run
equilibrium. Use the model to describe how each of the events will change the economy
in the long-run. Illustrate with diagrams.
a. An increase in personal taxes on households.
b. An increase in the quantity of money.
c. An increase in government purchases.
2.
The Liquidity Crisis and the Taylor Rule in Hong Kong. You are given the
following Table listing the output gap, the CPI and the overnight HIBOR Rate in Hong
Kong.
2007Q4
2008Q1
2008Q2
2008Q3
2008Q4
2009Q1
2009Q2
2009Q3
Output Gap
CPI
Inflation
xxx
107.4 xxx
0.049219808
108.2 0.029795
0.0299929
110.1
0.013160519
107.7
-0.013435423
109.6
-0.063140353
109.5
-0.037229897
109.2
-0.040702363
108.2
Interest Rate
Under
Taylor Rule
xxx
Actual
Interest
Rate
xxx
0.00781
0.00875
0.024375
0.00225
0.00375
0.0013
0.0013
a. For each quarter, construct the inflation rate on an annual basis. This is obtained just
P  Pt 1
by constructing the % growth rate of the price that occurs in a given quarter t
Pt 1
and then multiplying the result by 4. An example is constructed in the Table for the
1st Quarter of 2008.
b. Construct a hypothetical interest rate for HK with the Taylor rule using the CPI
inflation. CPI data and an assumption of an inflation target of 2%.
c. Compare the interest rate with that observed in HK. Note that the interest rate has
been below 1% in every quarter except the 2008Q3. Has the interest rate been higher
or lower in HK than that suggested by the Taylor rule?